Bill Shorten has reignited the education funding wars by promising to give the Catholic school sector an extra $250m in the first two years of a new Labor government.

In a move that could again make education funding into an election issue, the opposition leader has promised to stand “shoulder to shoulder” with Catholic schools in their increasingly bitter campaign against the government’s changes to education funding.

This week Shorten wrote to the Australian Catholic Bishops Conference chairman, Denis Hart, promising the sector would be $250m better off in the first two years of a Labor government and billions over the decade.

“We are committed to funding all schools based on a proper ­assessment of their need, while also supporting parental choice,” he wrote.

“Many low-fee Catholic schools are looking at doubling or even tripling their fees. We’ve seen very large falls in some areas, large falls in enrolments because schools are faced with increasing fees to this extent,” she said.

The Catholic sector is bitterly opposed to the new funding deal because it was designed to remove elements of the current formula that look at the average socio-economic status of all the schools in the sector rather than individual schools.

The Catholic sector says the SES system that formulates how much parents are able to pay toward their child’s education disadvantages their schools compared with the richest private schools.

The education minister, Simon Birmingham, was forced to wrangle a reluctant cross-bench while staring down an internal revolt from conservative Coalition MPs concerned about cuts to Catholic schools. The review is due to report in the middle of this year.

On Friday Birmingham accused Labor of abandoning the principle of needs-based funding and said Shorten was promising a “special deal” for one part of the school sector.

“I think that Catholic parents, teachers and principals are bigger and better than what Bill Shorten is trying to appeal to,” he said. “That he is out there saying we can buy you off with a special deal, whereas I believe that people want to see a fair and transparent system and also one that is enduring.

“Bill Shorten’s letter talks about what might happen over the next one or two years, but there is no certainty beyond that. Whereas the model the Turnbull government sought to put in place by building it around what David Gonski had recommended is an enduring model.”